Spectrum of quasistable states in a strong microwave field

When atoms are exposed to intense laser or microwave pulses, $\sim 10\%$ of the atoms are found in Rydberg states subsequent to the pulse, even if it is far more intense than required for static field ionization. The optical spectra of the surviving Li atoms in the presence of a 38-GHz microwave field suggest how atoms survive an intense pulse. The spectra exhibit a periodic train of peaks 38 GHz apart. One peak is just below the limit, and with a 90-V/cm field amplitude the train extends from 300 GHz above the limit to 3000 GHz below it. The spectra and quantum-mechanical calculations imply that the atoms survive in quasistable states in which the Rydberg electron is in a weakly bound orbit infrequently returning to the ionic core during the intense pulse.

Figure 1

Experimental timing diagram for the investigation of the microwave recombination in Li by a 38.3-GHz microwave (MW) field.

Figure 2

Field-ionization signal as a function of laser frequency tuning, in terms of energy relative to the ionization limit (IL), after exposure to a microwave pulse of amplitude 0, 16, 36, and 45 V/cm. The horizontal axis is calibrated by the etalon and optogalvanic signals.

Figure 3

Field-ionization signal as a function of laser frequency, after exposure to a microwave pulse of amplitudes (a) 0 V/cm, (b) 36 V/cm, (c) 45 V/cm, (d) 63 V/cm, and (e) 90 V/cm. A 50-ns integration gate is used to detect only atoms bound within 75 GHz of the IL. The zero-field spectrum is scaled by a factor of 1/3 to fit the graph. Horizontal dotted lines show the zeros of the corresponding spectra. The traces are offset by the square root of the microwave field. The broken line connects the onsets of the peaks in the different spectra, and the energy of the onset obeys the relation $W=-4\sqrt{E}$.

Figure 4

Field-ionization signals as a function of laser frequency for excitation in the presence of a microwave pulse of amplitude 90 V/cm. (a) The total photoabsorption spectrum when detecting all energies above $n=43$. (b) Spectrum obtained when detecting only the high-lying states. The total photoabsorption spectrum is scaled by a factor of 8 to fit the graph. Horizontal dashed lines show the zeros of the corresponding spectra. The total photoabsorption spectrum also presents the 38-GHz structure at energies below $-1500$ GHz since only atoms transferred to higher-lying states are detected.

Figure 5

Field-ionization signal as a function of laser frequency tuning after exposure to a microwave pulse of 90 V/cm amplitude for different static fields in the interaction region: (a) 8 mV/cm, (b) 17 mV/cm, (c) 25 mV/cm, (d) 40 mV/cm, and (e) 55 mV/cm. A break is shown on the horizontal axis for convenience. Horizontal dashed lines show the baselines of the corresponding spectra. Vertical blue lines intersect the horizontal baselines at points to which the ionization limit is depressed due to $W=2\surd E$ for the corresponding static field $E$. The double headed arrow that is 19 GHz long is the difference in the depression of the limit by 40 and 8 mV/cm fields. It is apparent that peaks in the microwave structure also shift by $W$, irrespective of the laser frequency. Increasing the static field destroys the microwave structure, and the 55-mV/cm spectrum shows only noise, with no bound population detected.

Figure 6

Field-ionization signal as a function of microwave pulse duration after the laser excitation. The microwave pulse amplitude is 90 V/cm, and the laser frequency is fixed and tuned to (a) two MW photons above the ionization limit and (b) 60 photons below it. Only the very high-lying states are collected with a 50-ns gate. The lifetimes exhibit an initial rapid decay followed by a very slowly decaying tail. The solid lines represent fits to the form $A{e}^{-x/t}+c$. According to the fit, the lifetimes of decaying exponentials are 68(10) and 107(10) ns, respectively.

Figure 7

Calculated spectra for a $9\times {10}^5$-V/cm 38-THz field from scaled one-dimensional quantum simulations at three different turnoff times for the microwave field. We smoothly turn off the microwaves to mimic the experimental conditions and wait until the field strength drops below ${10}^{-8}$ V/cm before we compute the surviving norm. The dotted blue curves show the spectra obtained when all bound states are detected, and the solid red curves show the spectra obtained when only bound atoms within 38 THz of the limit are detected. These spectra should be compared to Fig. 4. The only difference should be the units of the horizontal scale, THz instead of GHz.

Figure 8

The squared wave function 256 microwave cycles after the excitation pulse. There is substantial amplitude at small $x$ and again at $x\sim \pm 900$ a.u. The peaks at $\pm 900$ a.u. are persistent, whereas the small $x$ part of the wave function decreases for sufficiently long microwave exposure. The peaks at $x=\pm 900$ a.u. are located at the classical turning points of $n=21$.